**Title:** The Faber Polynomial Expansion Method for a Subclass of Analytic and Bi-Univalent Functions Associated with the Janowski Functions

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-20-00006; **Volume 3 / Issue 3 / Year 2021 (Special Issue)**, Pages 17-24

**Document Type:** Research Paper

**Author(s):** Nazar Khan ^{a} , Qazi Zahoor Ahmad ^{b}, Shahid Khan ^{c} , Bilal Khan ^{d}

^{a}Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan

^{b}Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan

^{c}Department of Mathematics Riphah International University Islamabad, Pakistan

^{d}School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, People’s Republic of China

Received: 27 March 2020, Accepted: 1 December 2020, Published: 25 April 2021.

**Corresponding Author:** Nazar Khan (Email address: nazarmaths@gmail.com)

**Full Text:** PDF

**Abstract**

In this present investigation, we introduce a new subclass of analytic and bi-univalent functions associated with Janowski functions. Using the Faber polynomial expansions, we determine a general coefficients bounds |*a*_{n}|, *n* ≥ 3 for this newly defined class. Relevant connections of the results presented in this paper with those in a number of other related works on this subject are also pointed out.

**Keywords:** Analytic functions, Univalent functions, Bi-univalent functions, Faber polynomial expansion

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